Conjugation Property and Conjugate Symmetry
The conjugation property states that if the $ \mathcal{F} $ of x(t) will be equal to X(jw) then, the $ \mathcal{F} $ of x*(t) will be equal to X*(-jw) This property follows from the evaluation of the complex conjugate of $ X^* (jw)=[\int\limits_{-\infty}^{\infty}x(t)e^{(-\jmath wt)}dt]^* $ $ X^* (jw)=\int\limits_{-\infty}^{\infty}x^* (t)e^{(\jmath wt)}dt $ Replacing w with -w, $ X^* (-jw)=\int\limits_{-\infty}^{\infty}x^* (t)e^{(-\jmath wt)}dt $
